On Faces of Quasi-arithmetic Coxeter Polytopes

@article{Bogachev2020OnFO,
  title={On Faces of Quasi-arithmetic Coxeter Polytopes},
  author={Nikolay Bogachev and Alexander Kolpakov},
  journal={arXiv: Geometric Topology},
  year={2020}
}
We prove that each lower-dimensional face of a quasi-arithmetic Coxeter polytope, which happens to be itself a Coxeter polytope, is also quasi-arithmetic. We also provide a sufficient condition for a codimension $1$ face to be actually arithmetic, as well as a few computed examples. 
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